US5563906A

US5563906A - Method of geometric harmonic modulation (GHM)

Info

Publication number: US5563906A
Application number: US08/407,560
Authority: US
Inventors: John E. Hershey; Gary J. Saulnier; Amer A. Hassan
Original assignee: General Electric Co
Current assignee: General Electric Co
Priority date: 1995-03-20
Filing date: 1995-03-20
Publication date: 1996-10-08
Anticipated expiration: 2015-03-20

Abstract

The present invention provides a novel Geometric Harmonic Modulation (GHM) method. The GHM method functions in two modes, a preamble mode and a traffic mode. During the preamble mode, n+1 frequencies are each offset by a predetermined phase in a transmit unit and passed through a channel to a receive unit. The set of phases is used as the spreading code in the transmit unit, and also acts as an `address` of intended receive units. The receive unit monitors preamble signals to determine the phases. When it recognizes a set of phases, or `address`, which pertains to itself, the receive unit stores the phases and uses these phases to despread and decode the appended message. After the preamble mode is finished, the GHM modulator enters the traffic mode and requests the message to be transmitted from the message source. A traffic carrier waveform is created by multiplying tones, each having its specific phase. An analog or binary message is encoded by modulating the traffic carder waveform. The receive unit detects a preamble carrier and recovers the particular preamble phases to be used as the despreading `key`. The receive unit then employs the phases in despreading the received signal to recover the transmitted binary message.

Description

CROSS REFERENCES TO RELATED APPLICATIONS

This application is related to U.S. Patent applications "Geometric Harmonic Modulation (GHM)--Analog Implementation" Ser. No. 08/407,088, "Geometric Harmonic Modulation (GHM) For Combined Analog/Digital Transmissions" Ser. No. 08/407,555, "Geometric Harmonic Modulation (GHM)--Digital Implementation" Ser. No. 08/407,554 by Hershey, Saulnier, Hassan; "Dynamic Code Division Multiple Access Communication System" Ser. No. 08/407,552 by Hershey, Hassan, Saulnier; "Correction Of Multipath Distortion In Wideband Carrier Signals" Ser. No. 08/407,559 by Hershey, Saulnier; and "Interlaced Geometric Harmonic Modulation" Ser. No. 08/407,551 by John Hershey all filed Mar. 20, 1995 all assigned to the present assignee and hereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to electronic signal modulation, and more specifically, to spread spectrum modulation.

2. Description of Related Art

Many systems provide for a plurality of transmitter and receiver pairs, "communicating pairs", to communicate simultaneously with little or no interference between communicating pairs. This may be accomplished by allocating a different communication frequency range to each communicating pair, known as frequency division multiple access (FDMA). There are situations in which it is difficult or impossible to assign each communicating pair a unique frequency. This occurs when there are simply too many communicating pairs close to each other on a designated bandwidth.

Another access method, such as time division multiple access (TDMA), may be employed, wherein each communicating unit is assigned a "time slice" in which to communicate on the same frequency band. This causes the "time slices" to become shorter as the number of communicating pairs increases.

Since both FDMA and TDMA communicate on narrowly defined bands, they are both susceptible to narrowband interference. Another method spreads each message from each communicating pair across the entire usable bandwidth. They are all specially encoded such that they may be separated at the receiver. These are known as code division multiple access (CDMA) spread spectrum techniques.

Spread spectrum techniques are those modulation techniques which require a transmission bandwidth that far exceeds the message information bandwidth. The spread spectrum modulation characteristics should not depend upon the individual message to be transmitted as is the case with some other wideband modulation schemes such as wideband FM. There are many spread spectrum mechanisms. They can be conveniently classified as: (i) direct sequence, (ii) frequency hopping, (iii) time hopping, and (iv) hybrids.

In direct sequence spread spectrum modulation, a wideband carrier signal is combined with the relatively narrowband message to yield an encoded wideband signal. A typical digital implementation would be to create a high speed pseudorandom binary sequence having an equal probability of being a one or zero at any particular time. This high speed binary sequence is added to a binary message sequence. The addition is typically done by exclusive-ORing ("XOR") the two sequences together. The bits of the message sequence are much longer in duration than the bits from the high speed pseudorandom source and thus many pseudorandom bits are used per information bit. The pseudorandom bits are often referred to as "chips" and the relationship between the pseudorandom sequence rate and the message rate is such that an integral number of chips are used per message bit. The code used to "spread" the signal at the transmit unit, is required in "despreading" the signal at the receive unit.

Many types of direct spread spectrum modulation techniques require binary data and require an extra step of digitizing an analog signal desired to be transmitted. After the digitized message is received at a receive unit, a binary message is recovered and an analog signal is reconstructed from the binary signal. This results in several conversions, each conversion possibly losing some information.

There are many uses for direct sequence spread spectrum techniques. One primary use is that of spectrum sharing. It is possible for a number of different communicating pairs to occupy the same bandwidth simultaneously without significant mutual interference. This is usually accomplished in direct sequence spread spectrum systems by assigning each communicating pair a different spectrum spreading code. This was described above as CDMA.

Typically, one problem with direct sequence spread spectrum communications and CDMA is synchronization. In order to function properly, the receiver must generate a copy of the spreading code at the same rate as the transmit unit. The receive unit must also correct relative phase discrepancies between the transmit and receive unit. This requires synchronization to be established and maintained at a tolerance finer than a single chip width. Further, the receiver must know the particular spreading code employed by the transmit unit in order to despread the signal and recover the message.

Currently there is a need for a simplified method of direct spread spectrum modulation of both binary and analog message signals which is not as sensitive as conventional systems to synchronization, and which does not require that the receiver know the spreading code in advance.

SUMMARY OF INVENTION

The present invention performs spread-spectrum modulation/demodulation in a simplified manner requiring less complex and powerful hardware. Phases φ₀, φ₁, φ₂, . . . φ_n are used as an `address` and also as the spreading code. During a preamble mode, a preamble signal is sent comprised of a fundamental frequency, or tone, and n higher frequencies, or tones each having a phase of φ₀, φ₁, φ₂, . . . φ_n, respectively. A receive unit monitors the preamble signals to determine when a message having the proper `address` is encountered. The set of phases φ₀, φ₁, φ₂, . . . φ_n, or `address`, is stored to be employed in the despreading of the signal.

In a "traffic mode", the tones are each offset by the corresponding phase and multiplied by each other to form a traffic carrier waveform W(Φ,R;t) during spreading in the transmit unit. Traffic carrier waveform W(Φ,R;t) results in 2ⁿ frequencies being the odd geometric harmonic multiples of the fundamental tone. R defines the extent of bandwidth spreading.

A binary message to be transmitted is used to cause a π phase shift of all frequencies for a bit period, which inverts the traffic carrier waveform, for a bit value of one; and causes no shift, or inversion, for a bit value of zero.

At the receive unit, the phases are extracted during the preamble mode, and are used to construct a reference signal to be compared with the received signal. The comparison produces either a correlation of approximately 1 or -1, meaning that the signal matches, and is inverted, respectively. This comparison is converted on a bit by bit basis into the transmitted binary message.

In the case of an analog signal m(t) being transmitted, traffic carrier waveform W(Φ,R;t) is frequency or phase modulated. The receiver then produces the same reference carrier waveform and demodulates the analog signal, directly.

In still another embodiment, a sensor detects if the input signal is a binary signal b.sup.(k), or an analog signal m(t), then activates a multiplier to invert the traffic carrier signal based upon binary signal b.sup.(k), or a analog signal modulator for frequency or phase modulating traffic carrier signal, respectively. This allows both analog and digital messages to be transmitted by the same direct spread spectrum device.

Since the present invention performs direct spread spectrum communication without the use of pseudorandom bits or `chips`, the synchronization is not necessarily as difficult as conventional direct sequence spread spectrum systems. Also, since all tones are multiples of a fundamental tone, having a phase of zero, following the fundamental tone allows for simplified synchronization.

The present invention is particularly applicable to spread spectrum code division multiple access (CDMA) communication. Many communicating pairs may occupy the same bandwidth simultaneously with little interference. On the average, the amount of interference increases smoothly as the number of communicating pairs increases. There is little overhead organization required, as compared with time division multiple access (TDMA), and there is also no need to have the receive unit know the despreading code in advance. There is also flexibility in using the `address` to apply to multiple receive units, to different message types, or to identify the originating transmit unit.

OBJECTS OF THE INVENTION

An object of the present invention is to provide a method of simplified modulation and demodulation of both binary or analog message signals for communication purposes.

Another object of the present invention is to provide a direct spread spectrum communications system capable of transmitting binary or analog signals.

Another object of the present invention is to provide a method of low power spread spectrum communications.

Another object of the present invention is to provide a code division multiple access system which does not require prior knowledge of the spreading code to recover a transmitted message.

Another object of the present invention is to provide a system for spread spectrum communication which is less sensitive to synchronization errors than conventional systems.

Another object of the present invention is to provide a method of spread spectrum communications which may be employed on less complex equipment as compared with conventional methods.

BRIEF DESCRIPTION OF THE DRAWINGS

While the novel features of the invention are set forth with particularity in the appended claims, the invention, both as to organization and content, will be better understood and appreciated, along with other objects and features thereof, from the following detailed description taken in conjunction with the drawings, in which:

FIGS. 1a, 1b, 1c are graphs of the wave function W_n (0,1;t) for n=0,3,6, respectively, used in connection with explaining the present invention.

FIG. 2 is a simplified block diagram of a first embodiment of a communications system according to the present invention.

FIG. 3 is a more detailed block diagram of receive unit 80 of FIG. 2.

FIG. 4 is a simplified block diagram of a second embodiment of a communications system according to the present invention.

FIG. 5 is a more detailed block diagram of receive unit 80 of FIG. 4.

FIG. 6 is an graph of probability of error vs. the number of users of the present invention transmitting a binary signal b.sup.(k).

FIG. 7 is a graph of the kurtosis of the power of the composite transmitted signal according to the present invention for 1 to 200 users for n=7.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Consider that the system supports a number of simultaneous users. Each user of the system signals one bit per symbol time defined as the reciprocal of the signaling rate R. (If an analog message is sent, R represents the extent of bandwidth spreading.) The signaling waveform is a member of {W_n (Φ,R;t)} where ##EQU1## where n is the "order" of the function, Φ=(φ₀,φ₁, . . . φ_n), and ##EQU2##

For finite order, n, the functions and all of their derivatives are continuous in the interval ##EQU3##

FIG. 1a, 1b, 1c illustrate representative waveforms of 2^n+1/2 W(Φ,1;t), namely W₀ (0,1;t), W₃ (0,1;t) and W₆ (0,1;t), respectively, where 0 indicates that all of the phases φ_i are zero. (For these examples, R=1).

If {b.sup.(i) (m)} is the binary message sent by the i-th user, the i-th user signal can be expressed as s.sup.(i) (t)=b.sup.(i) (m)W_n (Φ,R;ξ)δ([ξ.sup.(i) ]) where ξ.sup.(i) =R(t-τ.sup.(i))-m, τ.sup.(i) is the time of the start of the i-th transmission, [.] is the greatest integer function, and where δ(.) is the Kronecker delta function.

The composite signal, S(t), is then: ##EQU4## where N is the number of users. By writing ##EQU5## it is easily seen that Equation (1) can be expanded into a sum as ##EQU6## where A=(α₀, α₁, . . . , α_n) is a binary representation of the summation index

k with: ##EQU7## Θ(k), k=0,1,2, . . . is the Thue-Morse sequence. The Thue-Morse sequence can be thought of as the diagonal elements in the infinite Cartesian product ##EQU8## where H_n =H_n-1 ⊕H₁ and ##EQU9## (The first eight values, Θ(0)-Θ(7), are (1,-1,-1,1,-1,1,1,-1).

When a message is to be sent, the transmit unit enters the synchronization or preamble mode. For an environment wherein them is negligible multipath, the transmit unit transmits a preamble signal for a series of cycles. A cycle is defined as the duration of time delimited by two successive negative to positive zero crossings of the lowest frequency of the preamble signal.

A frequency of a master sinusoidal signal, or tone is selected. The master tone is divided down to produce frequencies of a plurality of tones, the lowest tone being a fundamental tone. Alternatively, a fundamental sinusoidal signal, or tone, having a fundamental frequency 2 πf₀ is selected. A plurality of tones are selected having frequencies which are geometrically progressing multiples of a fundamental frequency,, 2 πf₀ to result in n+1 tones.

Phases Φ={φ_i, i=1, 2, 3 . . . n} for each of the tones, except for the fundamental tone which has a phase of zero, are selected. The phases Φ in a preferred embodiment, are either of two substantially separated values, such as 0 and -π/2 radians, which may be selectable by an operator Phases Φ are used as the spreading code for spreading an input signal across a frequency spectrum, and for despreading the signal at a receive unit. A preamble carrier waveform is constructed by summing the tones, each incorporating its phase. The preamble carrier waveform has the full transmit power distributed over the n+1 frequencies.

The phases Φ may also be used as an operator selectable `address` of an attached message. In one possible embodiment, each receive unit knows its own `address`. The receive unit constantly monitors preamble signals to identify the phase `address`. If it encounters an `address` which matches its own, it then despreads and decodes the appended message using its `address`.

In an alternative embodiment, the phases Φ define a transmit unit ID. Each receive unit knows which transmit unit to `pay attention to` at a given point in time. If the phase `address` matches a transmitter which the receive unit is supposed to listen to, it despreads and decodes this appended message.

In still another embodiment, the phase `address` is used to identify message types. Each receive unit knows which message type to monitor in a given situation. For example, a `broadcast` message type `address` will be received by all receive units, with a `group 2` message type being despread and decoded by receive units which are presently designated as `group 2` receive units, while other receive units presently designated as `group 1` or `group 3` will ignore the message.

After completion of the preamble mode, the present invention enters the signaling, or traffic, mode. A traffic carrier waveform is constructed as the product of the tones, incorporating their phases.

In the example of FIG. 2, an analog circuit of a transmit unit 10 compatible with the present invention is shown.

A reference oscillator 2 of a transmit unit 10 produces a signal, such as a sine wave of a frequency 2ⁿ *2 πf₀. This reference sine wave is provided to a plurality of

branches

1, 3, 5, 7, 9. Only five branches are shown here, but it is to be understood that will be n+1 branches, with the branch of the lowest frequency component 2 πf₀ having a phase φ₀ of 0.

Frequency dividers

13, 15, 17, 19 divide the frequency of the sine wave of previous branches in half to result in n+1 sinusoidal signals or `tones`.

Phase devices

21, 23, 25, 27 provide a predetermined phase, here being -π/2, to selected tones. Branch 9 with the fundamental tone having a frequency 2 πf₀, will in the preferred embodiment, always be set to a phase of zero, thereby resulting in only n phases instead of n+1.

Switches

31, 33, 35, 37 are switched to either incorporate the phase of devices 21-27, or not to incorporate these offsets. Switches 31-37 are set to correspond to a predetermined address, or despreading `key`.

Delta gates

41, 43, 45, 47 act as summers when transmit unit 10 is operating in a preamble mode, and act as multipliers in the traffic mode. The delta gates may be collectively referred to as a combining device. If n is selected to be 5, then 6 tones, each with their own phase φ_l are transmitted by transmit unit 10 during the preamble mode.

After transmit unit 10 enters the traffic mode, delta units 41-47 act as multipliers creating 2ⁿ =2⁵ =32 tones, with each tone having a phase, for n selected to be 5.

A modulator 51 encodes a message signal into the traffic carrier. In the case of a binary message signal b.sup.(k) to be transmitted, modulator is a multiplier, and binary message b.sup.(k), converted to a series of -1, 1 values, representing the two logical values of a binary signal. Binary message b.sup.(k) is fed to the modulator 51 which inverts or does not invert traffic carrier waveform W_n (Φ, R;t) for a whole bit period, being 1/R. The preamble waveform transmitted during the preamble mode is the sum of tones, each being a geometrically increasing multiple of a fundamental frequency 2 πf₀. Whereas the traffic carrier waveform W_n (Φ,R;t) is the product of these tones, or which result after multiplication by the delta units. This results in the odd harmonics, 6 πf₀, 10 πf₀, 14 πf₀, . . . The fundamental frequency 2 πf₀ is also used as the lowest frequency component having a 0 phase.

For transmission of an analog signal a(t), modulator 51 is a frequency, or phase modulator encoding the analog signal a(t) into the traffic carrier waveform W_n (Φ,R;t).

A complex signal f(t) from modulator 51 is upconverted by an up converter 53 to produce a signal transmitted to a plurality of receive units 80.

In FIG. 3, a more detailed block diagram of the receive unit 80 of FIG. 2 is shown. A front end 84 down converts the signal received during the preamble mode r^p (t), and a signal received during a traffic mode, r^t (t). A phase-locked loop (PLL) 119 tracks the fundamental frequency of the received signal and creates a time changing error signal which is used by a preamble/traffic mode estimator (P/T mode estim.) to adjust the phase of a master oscillator 82 in order to minimize the difference in phase. Master oscillator 82 is adjusted throughout the preamble mode. Thus, receive unit 80 establishes a phase reference by which it can estimate the phases of the n other sine waves.

P/T mode estim. 117 monitors even harmonics of the fundamental frequency 2 πf₀ for preamble signals and notifies elements of the receive unit 80, such as a compare and integrate unit 115, that it is now in preamble mode. When the preamble mode is over, master oscillator 82 runs without further correction, i.e., it "flywheels" through a traffic mode.

Master oscillator 82 creates a sinusoidal reference signal which is stepped down by frequency dividers 83-89 to create a set of reference tones. Each

frequency divider

93, 95, 97 passes its reference tone to phase estimators 103, 105, 107 of

branches

83, 85, 87, respectively. Each phase estimator compares its reference tone to a corresponding frequency component of the received signal during preamble mode r^p (t) to estimate a preamble phase φ_i for this tone. Since the phase of the fundamental tone is set to zero, branch 89 has no phase estimator. Also, branch 81 has a phase estimator which receives its signal directly from reference signal generator 82, and not from a frequency divider.

The set of phases, Φ, denote both an `address` and determine the spreading code. Once the set of phases is acquired during the preamble mode, they are stored. If the phases Φ correspond to an `address` which receive unit 80 is searching for, a message immediately following the preamble signal is despread and decoded using the phases Φ acquired during the preamble mode.

Once the traffic mode begins, the phases Φ are employed in the tones of their respective branches, and the tones and offsets are provided to a sine product generator 113. Sine product generator 113 multiplies the tones to create the complex carrier waveform W_n (Φ,R;t) having the `address`, or spreading code, incorporated into it, which is then provided, along with the signal received during the traffic mode, to a decoding unit, 116.

In the case of a binary message b.sup.(k) being decoded, decoding unit 116 has compare and integrate unit 115, and a decision device 121.

Compare and integrate unit 115 correlates the complex carrier waveform W_n (Φ,R;t) with the received signal r^t (t) and integrates the correlation result over all tones, and over the entire data bit duration.

The output of the compare and integrate is passed to a decision device 121 which compares the result of the integration to a threshold. If the integration result is above the threshold, a logical bit value is output, and if not, a second logical value is output. This results in a logical bit stream b.sup.(k).

If receive unit is to decode an analog signal encoded in traffic carrier waveform W_n (Φ,R;t), decoder 116 may be a conventional frequency demodulator, or a phase demodulator, corresponding to a frequency modulator, or phase modulator used as modulator 51 in transmit unit 10, respectively.

Since all tones employed by the present invention are multiples of a fundamental tone, and the fundamental tone has a phase of zero, synchronization is much simpler than conventional direct spread spectrum systems.

Also, the implementation described above is a very simple circuit, having low power requirements allowing it to be employed in remote areas where spread spectrum technology is required, and where line power is not available and run from a battery.

FIGS. 4, 5 represent another embodiment of the present invention. The same-numbered elements of FIGS. 4, 5 function as their counterparts in FIGS. 2, 3. Modulator 51 has been replaced with a input sensing device 38 a switching unit 42, a multiplier 52 and a modulator 54. Modulator 54 may be a conventional frequency or phase modulator. Input sensing device 38 receives a time changing message m(t) which may be analog, a(t), digital b.sup.(k), or both interleaved, and determines if the next message to be transmitted is binary b.sup.(k) or analog a(t). If the message is binary, input sensing device activates switching device 42 such that multiplier 52 receives the binary message b.sup.(k) and traffic carrier waveform W_n (Φ,R;t) from delta unit 41 thereby causing it to invert or not invert the carrier waveform based upon binary message b.sup.(k).

If input sensing device 38 determines that the next message to be transmitted is an analog signal a(t), it activates switching device 42 to provide analog signal a(t) to modulator 54 to modulate traffic carrier waveform W_n (Φ,R;t) according to analog message signal a(t).

The advantage of this embodiment of the present invention is to make efficient use of airtime. Binary messages b.sup.(k), data, may be transmitted during `air gaps` in speech or audio transmissions. This may be the majority of the transmission time and result in a great deal of data transfer. The data transfer may be used to transmit images, tables or other information referenced in an audio conversation.

In FIG. 6, the performance of the present invention having a waveform of order n=7 is compared to that of coherent phase shift keying (CPSK). The results of error rate of the present invention using a waveform of order n=7, versus the number of other active users is shown as the solid line plot of FIG. 6. This was achieved with assuming unit energy per bit, E_b =1.

The background noise from the m other active users can be modeled as Gaussian, and set:

N.sub.0 =m·2.sup.-n                               (5)

then, in Gaussian noise, the CPSK probability of error rate p_e, may be approximated by: ##EQU10## where energy/bit E_b =1 and N₀ is as defined in Eq. (5) above. The plot of CPSK is shown as the dotted line on FIG. 6.

Therefore it can be seen that the error rate of the present invention increases gradually with increased number of users. It can also be seen that the error rate of the present invention with approximately 50 users and n=7 is about the same as the predicted error rate of a conventional CPSK system.

As can be seen from the example n=6 signaling waveform shown in FIG. 1c, the signal of each individual user of the present invention has, generally speaking, a high dynamic range of the envelope. A composite signal which is the sum of randomly selected signals having randomly selected phases has a much reduced dynamic range of the envelope. A rough simulation was done with n=7 and users picking waveforms randomly. The power of the composite signal, which is what the transmit unit must transmit, was estimated as well as the kurtosis of the signal to see how close it might be to the Gaussian kurtosis of 3. FIG. 7 displays the results for 1 to 200 users.

Note that the composite signal kurtosis becomes very close to that of a Gaussian when the number of users is at least about 50 for n=7.

While several presently preferred embodiments of the novel invention have been described in detail herein, many modifications and variations will now become apparent to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and variations as fall within the true spirit of the invention.

Claims

What we claim is:

1. A method of communicating a binary input stream b.sup.(k) from a transmit unit to a receive unit comprising the steps of:

a) selecting a frequency of a fundamental tone;

b) selecting a plurality of tones having frequencies higher than the fundamental tone

c) selecting a phase for each tone except the fundamental tone for which a phase of zero is selected;

d) applying each phase to its corresponding tone to result in offset tones;

e) summing the offset tones to produce a preamble carrier waveform;

f) transmitting the preamble carrier waveform from said transmit unit to said receive unit;

g) extracting the phases from the preamble carrier waveform at the receive unit;

h) multiplying the offset tones to create a traffic carrier W_n (Φ,R;t);

i) encoding said binary stream b.sup.(k) in carrier waveform W_n (Φ,R;t) to result in an encoded carrier waveform;

j) transmitting the encoded carrier waveform from said transmit unit to said receive unit; and

k) despreading the encoded carrier waveform employing the extracted phases as a despreading key at said receive unit.

2. The method of communicating a binary input stream b.sup.(k) of claim 1 wherein the step of extracting the phases from the preamble carrier waveform comprises the steps of:

a) synthesizing a fundamental reference tone and a plurality of reference tones all having frequencies the same as the tones of the transmit unit;

b) applying a phase to one of the reference tone other than the fundamental reference tone to result in an offset reference tone;

c) correlating the preamble carrier to this offset reference tone to determine a correlation;

d) repeating steps "b" and "c" for a plurality of possible phases to determine the phase corresponding to a highest correlation;

e) assigning the phase with the highest correlation to this tone; and

f) repeat steps "b"-"e" for all reference tones except the fundamental reference tone which has a phase of zero.

3. The method of communicating a binary input stream b.sup.(k) of claim 1 wherein the step of despreading the encoded carrier comprises the steps of:

a) synthesizing a set of reference tones having the same frequencies as those of the transmit unit;

b) applying the phases extracted from the preamble carrier waveform to their corresponding tones to result in offset reference tones;

c) multiplying the offset reference tones and the fundamental tone to result in a reference traffic carrier waveform W_n (Φ,R;t); and

d) comparing the reference traffic carrier waveform W_n (Φ,R;t) to the encoded carrier waveform transmitted from said transmit unit to determine logical bit values of binary input stream b.sup.(k).